Arithmetic differential geometry in the arithmetic PDE setting II: curvature and cohomology

2022/12/06 by Buium, Alexandru, Miller, Lance Edward
#Differential Geometry (math.DG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2212.02697

Abstract

This is the second paper in a series devoted to developing an arithmetic PDE analogue of Riemannian geometry. In Part 1 arithmetic PDE analogues of Levi-Civita and Chern connections were introduced and studied. In this paper arithmetic analogues of curvature and characteristic classes are developed.

Related

• Arithmetic differential geometry in the arithmetic PDE setting, I: connections
• Arithmetic analogues of some basic concepts from Riemannian geometry
• Curvature on the integers, I
• Curvature on the integers, II
• The geometry of second-order ordinary differential equations